The limited proportion of complex trait variance identified in genome-wide association studies may reflect the limited power of single SNP analyses to detect either rare causative alleles or those of small effect. Motivated by studies that demonstrate that loci contributing to trait variation may contain a number of different alleles, we have developed an analytical approach termed Regional Genomic Relationship Mapping that, like linkage-based family methods, integrates variance contributed by founder gametes within a pedigree. This approach takes advantage of very distant (and unrecorded) relationships, and this greatly increases the power of the method, compared with traditional pedigree-based linkage analyses. By integrating variance contributed by founder gametes in the population, our approach provides an estimate of the Regional Heritability attributable to a small genomic region (e.g. 100 SNP window covering ca. 1 Mb of DNA in a 300000 SNP GWAS) and has the power to detect regions containing multiple alleles that individually contribute too little variance to be detectable by GWAS as well as regions with single common GWAS-detectable SNPs. We use genome-wide SNP array data to obtain both a genome-wide relationship matrix and regional relationship ("identity by state" or IBS) matrices for sequential regions across the genome. We then estimate a heritability for each region sequentially in our genome-wide scan. We demonstrate by simulation and with real data that, when compared to traditional ("individual SNP") GWAS, our method uncovers new loci that explain additional trait variation. We analysed data from three Southern European populations and from Orkney for exemplar traits - serum uric acid concentration and height. We show that regional heritability estimates are correlated with results from genome-wide association analysis but can capture more of the genetic variance segregating in the population and identify additional trait loci.